Can someone help me convert this (f(x)=9.75e^-0.43x) into a logarithmic function? Please.

Question

anonymous · Answer

Suppp.

anonymous · Answer

.... >.>

anonymous · Answer

Yeah bro what's up. lol

anonymous · Answer

I'm not a bro but the question is what's up there. See what I did there? lol.

amistre64 · Answer

log each side ...

anonymous · Answer

This what I have so far:
y=9.75e^(-0.43x)

4/9.75= e^(-0.43x)

In the example I have it says something about IN and I have no clue what that is.

amistre64 · Answer

LN, is an undergradute notation for a natural logarithm, in upper classes its just LOG, which i admit can be confusing

amistre64 · Answer

y=9.75e^(-0.43x)

ln(y) = ln(9.75e^(-0.43x))

ln(y) = ln(9.75) + ln(e^(-0.43x))

ln(y) = ln(9.75) -0.43x ln(e)

ln(y) = ln(9.75) -0.43x

ln(y)/ln(9.75) = -0.43x

anonymous · Answer

Thank you so much.

amistre64 · Answer

yep ... good luck ;)

anonymous · Answer

@amistre64 
check out this law of logarithms:

$$\ln(a) - \ln(b) =\ln( \frac{ a}{ b })$$

amistre64 · Answer

yes, and ln(ab) = ln(a) + ln(b) ...

amistre64 · Answer

...and it looks like a divided instead of subtracting;  i blame the ascii :)

amistre64 · Answer

ln(y) = ln(9.75) -0.43x

ln(y) -  ln(9.75) =  -0.43x

ln(9.75) - ln(y) =  0.43x